In the American context evangelicals are orthodox Protestant Christians, Christians who maintain belief in the supernatural work of God to save us from sin, including Jesus' virgin birth,miracles, atoning death, resurrection, and return. The Reformed also maintain these doctrines (with some slippage on both sides). Since they hold every doctrine that defines evangelicalism, they can be regarded as evangelicals. But of course they also believe some things that do not define evangelicalism, which makes them a distinct strand of the evangelical movement. [John Frame, The Escondido Theology: A Reformed Response to Two Kingdom Theology (Lakeland, FL: Whitefield Media Productions, 2011), 95]
Historically speaking, "evangelical" is the name used by Lutherans to describe themselves. The term then took on a new meaning when it came into widespread use as a name at the time of the First Great Awakening in Britain, as a description by Christians who believe that one must personally believe in Jesus Christ to be saved, in contrast to the general apostasy within the 18th century Church of England whereby many ministers do not even believe the Gospel much less teach and proclaim it. Evangelicalism therefore as a movement is a reaction to the unregenerate state of the 18th century Church of England. Unfortunately, the rejection of the apostate established church comes about without a recovery of Reformed church piety. When the First Great Awakening came to America, George Whitefield transplanted the entire British experience over such that all professing believers must be assumed to be unregenerate unless they have a conversion experience, resulting in the split within American Presbyterianism into the Old Side and the New Side.
"Evangelicalism" and "Evangelical" from then on refer to the movement that spawned from the 18th century Great Awakening. While it generally has similar doctrines to the Reformed faith, the major difference however is where they differ: ecclesiology. Evangelicalism never has a proper doctrine of the church, only a truncated doctrine of the local church and a spiritual doctrine of the universal church.
We see that John Frame thinks like an Evangelical. That is why he can talk so flippantly about "evangelical reunion," as if "evangelical" was primary. Of course, if one thinks only about doctrine, then Reformed seem to be a subset of Evangelicalism. But historically such is not the case. The Reformation was first, then the rise of Evangelicalism.
Frame's doctrine of the Church is not Reformed. That is why he can misunderstand R. Scott Clark's view of confessionalism, because for him there is no difference between the individual, and the group. He has no concept that the group, i.e. the institutional Church, is a distinct entity separate from the individuals even though it is made up of individuals. Frame therefore is stymied when Clark criticize his views as being individualistic when he defines Reformed as being "the consensus of Reformed believers" (p. 75, 81). There is a big difference between "the consensus of Reformed believers" and "the consensus of the Reformed Church made up of Reformed believers." The former focuses on the individual, such that a modification of Dr. Clark's syllogistic representation holds true ("a number of believers self-identify as Reformed, They hold X; X is Reformed"), while the latter focuses on the Church coming to its official pronouncement ("The Church, comprising many believers who self-identify as Reformed, wrote/adopt this Confession; The Confession state X; X is Reformed"). The failure of Frame to see this is astonishing, but I guess that is what happens when individualism is taken to the extreme such that the collective is denied. Lastly, Frame objects that the Confession has to be interpreted and thus subjectivism is still present, but such is a cop-out for the simple reason that the same argument can be applied to Scripture, yet Evangelicals still believe in the authority of Scripture instead of asking "Has God said?".
Frame may not like the Reformed doctrine of the Church; that is his perogative. But it is tiresome when he continues to insist that he is Reformed. Can someone who self-identifies himself as Reformed deny Reformed ecclesiology and still be Reformed? That is the crux of the matter, and that is why Frame's main critique of Clark is wrong.